JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A8, 10.1029/2001JA000099, 2002

Interplanetary magnetic field control of the entry of solar energetic

particles into the magnetosphere

R. L. Richard, M. EI-Alaoui, M. Ashour-Abdalla, l and R. J. Walker 2

Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, California, USA\

Received 2 April 2001; _yised 6 February 2002; accepted 18 March 2002; published 15 August 2002.

[_] We have investigated the entry of energetic ions of solar origin into the

magnetosphere as a function of the interplanetary magnetic field orientation. We have

modeled this entry by following high energy particles (protons and 3He ions) ranging from

0.1 to 50 MeV in electric and magnetic fields from a global magnetohydrodynamic

(MHD) model of the magnetosphere and its interaction with the solar wind. For the most

part these particles entered the magnetosphere on or near open field lines except for some

above I0 MeV that could enter directly by crossing field lines due to their large gyroradii.

The MHD simulation was driven by a series of idealized solar wind and interplanetary

magnetic field (IMF) conditions. It was found that the flux of particles in the

magnetosphere and transport into the inner magnetosphere varied widely according to the

IMF orientation for a constant upstream particle source, with the most efficient entry

occurring under southward IMF conditions. The flux inside the magnetosphere could

approach that in the solar wind implying that SEPs can contribute significantly to the

magnetospheric energetic particle population during typical SEP events depending on the

state of the magnetosphere. INDEX TERMS." 2720 Magnetospheric Physics: Energetic particles,

trapped; 2716 Magnetospheric Physics: Energetic particles, precipitating; 2753 Magnetospheric Physics:

Numerical modeling; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; KEYWORDS:

Solar energetic particles, magnetosphere, trapping, precipitation

1. Introduction

[2] Solar energetic particles (keV to GeV) are generated

at active regions on the Sun and are also accelerated at

interplanetary shocks launched by the solar disturbances

[Fliickiger, 199l; Shea and Smart, 1995]. These particles

can move along interplanetary magnetic field lines to the

Earth. Solar energetic particles (SEPs) can reach the ground(solar cosmic ray events), and enhanced proton fluxes can

be seen at the top of the atmosphere and in space (solar

proton events). It is well established that energetic ions can

penetrate the magnetosphere:[Fennell, 1973]. That particle

fluxes at geosynchronous orbit track those in the interplan-

etary medium "[Kallenrode, 1998] is evidence of deep

penetration of these particies; particularly the ions. It is

not presently clear,- however, how solar high energy p_ir-

lasting for days. While protons, electrons and c_ particles

dominate both kinds of events heavy ions and 3He ions are

also present. The two types of events are distinguished by

compositional and other differences indicating different

acceleration mechanisms. In particular the impulsive events

are rich in 3He. The gradual events are correlated with

coronal mass ejections that accelerate particles at their

accompanying shocks, and impulsive events that evidently

originate at solar flares [Reames, 1999].

" [4] Differential fluxes near 100 keV from a "typical"

gradua I SEP event in the heliosphere [Gloeckler et al.,

1984i Lin, 1987] are roughly comparable to those measured

in the high energy tail of the proton distribution in the

plasma sheet [Christon et al., 1988]. Reames et al. [1997]

shows a differential flux of a similar magnitude at 100 keV

for a gradual event on October 20, 1995 (105 protons/(cm 2ticles (>0.1 Me'_).enter, are transported within and exit the sr S MeV)). The distribution function for these protonsmagnetosphere [Gussenhoven_et al., 1996]. - ....

follows a power law distribution (f ,,_ E -v) with ",/ -_ 2.[3] There are two basic types of SEP events, gradual"and. Rodriguez-Pacheco et al. [1998] fit power laws to ion

impulsi_,e [Kallenrode, 1998; Reames, 1999; Blanc et,al.,, distributions between 36 and 1600 keV for the most intense

1999]. Impulsive events lasi for hours; whilegradual events, energeiic particle events of solar cycle 21, mostly gradual

as the name suggests, are typically longer in duration; _events, and found that these power law exponents ranged

_Also at Department of Physics and AstronomY, University ofCalifornia at Los Angeles, Los Angeles, Cali|brnia, USA.

"-Also at Department of Earth and Space Science, University ofCalifornia at Los Angeles, Los Angeles, California, USA.

Copyright 2002 by the American Geophysical Union.0148-0227/02/2001 JA000099509.00

from,1.25 to 1.94 with a mean of 1.60. Christon et al.

[.]988] found that the high energy part of the plasma sheet

spectra followed power laws with exponents around 6.5.Given that the differential fluxes of 100 keV ions in SEPs

and in the plasma sheet are comparable, and further if solar

energetic particles can penetrate the magnetosphere freely,

the much harder (lower power law exponents) SEP spectra

SSH 7- i

https://ntrs.nasa.gov/search.jsp?R=20030014815 2018-05-14T19:19:31+00:00Z

SSH 7 - 2 RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL

imply that these will dominate at higher energies. Note that

Christon et al. [1988] did not study particles with energies

as large as the more energetic SEPs, and this comparison is

partly based on extrapolating the plasma sheet energy

distributions. These simple estimates suggest that SEPs

can be an important component of the magnetospheric

particle population during strong SEP events, if they can

efficiently enter the magnetosphere. Observations of SEP

ions at geosynchronous orbit [Kallenrode, I998] confirm

that they can be an important energetic particle source.

[5] Internal acceleration within the magnetosphere during

disturbed times can also lead to high-energy injection

events. One example of this is the appearance of high

energy electrons in the 2 to 6 MeV range associated with

periods of high solar wind speed that has been attributed to

high inductive electric fields within the magnetosphere

[Baker et al., 1998]. Hudson et al. [1996] investigated ring

current formation by following high energy particles in the

equatorial plane in the inner magnetosphere in an MHDmodel to study how the electrons and protons were accel-

erated and transported into the ring current. They assumed

that the energetic protons were of solar origin and that they

had already penetrated the inner magnetosphere. They did

not consider how the ions reached this region, which is thetopic of this study.

[6] The goal of this study is to understand the entry of

SEPs into the magnetosphere and under what conditions

they contribute significantly to the magnetospheric particlepopulation. While the most energetic solar particles will not

be strongly deflected by magnetospheric magnetic fields,

the entry of a large fraction of the incoming energeticparticles will be influenced by the magnetospheric config-

uration, which is controlled in turn by the IMF. We will

approach the problem of SEP entry into the magnetosphere

by calculating the trajectories of many particle trajectories in

MHD field models of the magnetosphere under differentIMF conditions. We focus on the transport into the inner

magnetosphere that provides the source population tbr thering current rather than the evolution of that source pop-

ulation into the ring current population. In the section 2 of

this paper we discuss our model and in section 3 we presentour results. In section 4 we discuss what we have learned

about SEP ion entry.

2. The Model

[7] In this section we describe the model system we used

for our calculations. We computed the trajectories of high

energy particles subject to the Lorentz force equation

including relativistic modifications. Because these high

energy particles have large Larmor radii, a guiding center

approximation would be inadequate. The electric and mag-

netic field model in which we determined the trajectories of

these particles was obtained from a global magnetohydro-

dynamic (MHD) simulation of the magnetosphere and its

interaction with the solar wind [Raeder et al., 1995]. MHD

simulations provide the best three dimensional global mod-

els of the entire magnetosphere and its interaction with the

solar wind available, as shown by their ability to model

spacecraft observations [Frank et al., 1995]. MHD simu-lations have been used with some success as field models in

which to model thermal particle motion in the magneto-

sphere [Richard et al., 1994, 1997; Ashour-Abdalla et al.,

1997]. SEP particles in the solar wind are very tenuous

compared to the bulk (low energy) solar wind and they

should not perturb the field model significantly, with the

possible exception of the ring current region. For this study

we primarily launched protons, but we also launched some

3He ions because of their importance as indicators of

impulsive solar particle events.

[8] To simplify the interpretation of the results we used

idealized solar wind and 1MF conditions (Figure 1) to drive

the simulation. The y and z components of the IMF were

assumed to vary during the simulation (Figure 1) while the

IMF x component was held at -5 nT. For the first hour and

a half of the simulation, B z was southward with a magnitude

of 5 nT to initialize the simulation. From 1.5 to 3.5 hours Bz

was southward with a magnitude of 8 nT. A two hour

interval of steady IMF allowed the model magnetosphere to

respond to this driving condition. Previous MHD simula-tions have shown that a timescale of one to two hours is

needed for the magnetosphere to reach a new configuration

following a change in the IMF [Ogino et al., 1994; Walker

et al., 1999]. During this southward IMF interval solar

wind, i.e. not connected to the Earth, field lines reconnected

with closed field lines on the dayside, while in the magneto-

tail open field lines reconnected to make solar wind and

closed field lines. We varied the IMF linearly in time

between 3 hours 30 min and 4 hours until it was dawnward

and then held it steady with By = 8 nT from hours 4 to 6.

This led to a magnetospheric configuration with open field

lines on the dawn side flank of the magnetosphere. From

hour 6 to 6 hours 30 rain the IMF changed to northward

IMF and remained steadily northward with a magnitude of 8

nT until hour 8. For northward IMF conditions reconnection

occurred tailward of the cusp. In general the magnetospheric

configurations were similar to those seen in previous MHD

simulations fbr idcalized IMF conditions [e.g., Walker and

Ogino, 1989]. Particles were launched for a longer interval

of time in the northward and dawnward IMF configurations

than in the southward based on the assumption that during

the first three hours of the simulation the magnetosphere

had already responded to the southward IMF condition.

Other solar wind parameters did not change with time. The

solar wind density remained fixed at 10 cm -3, and its

velocity was -450 km/s in the x direction and the thermal

pressure was 20 x 10 -12 Pa. One feature of the simulation

that was not included in many idealized simulations was a

constant magnetic dipole tilt angle of 33 ° . The resulting

hemispheric asymmetry was increased further because of"

the presence of an 1MF B×. Besides tilting the dayside

magnetosphere the tilt and the B_ depressed the plasma

sheet below z = 0 and warped it downward in the center

versus the flanks.

[9] The entry of the high energy particles into the

magnetosphere is strongly affected by the presence of open

magnetic field lines. The variation of the fraction of open

magnetic flux on the inner boundary as a function of time

(Figure 2) reflects the morphological evolution of the model

magnetosphere. For southward IMF the fraction of openflux is more than half. After the transition to dawnward IMF

the traction of open flux decreased for about 45 min and

then stabilized and increased slightly. After the transition to

northward IMF the fraction of open magnetic flux decreased

RICHARDETAL.:INTERPLANETARYMAGNETICFIELDCONTROL SSH 7 - 3

MHD Input Parameters

A

I-

-10 ! • . , . . • , • . . , . . • , • . , • • • , . • • , • • •10

A

0 1 2 3 4 § 8 ?

Time (Hours)

Figure I. MHD input parameters. This figure shows the IMF conditions used to drive the MHD

simulation as a function of time.

to an even lower level. Overall we arranged the simulation's

driving conditions to be appropriate for generating a series

of representative magnetospheric states. Launching a con-

stant upstream flux in this system allowed us to attribute

changes in the particle population in the magnetosphere to

the effect of the magnetospheric configuration.

[10} The particle trajectories were calculated in the time

varying fields from the MHD simulation and they experi-

Fraction of magnetic flux on open field lines

C0D,0

Oc_m

q,w

Um

o

So We No

,... ]i

. ' ' I ' ' ' I ' ' ' I '

6 7 8

a 4 HouSs(UT)r

Figure 2. Fraction of open magnetic flux as a function of time. This was calculated by integrating the

amount of open and closed flux through the inner boundary sphere at 4.5 R E and dividing the amount of

open flux by the total. The shaded bands indicate the times when the lMF was changing. The IMFdirection is also indicated: "So" stands for southward, "We" for dawnward and "No" for northward.

SSH 7- 4 RICHARDETAL.:INTERPLANETARYMAGNETICFIELDCONTROL

O

O

O

O

\

\

\

°v \

,q,|

20 10 0 -10 -20 -30 -40 -50 -60 -70 -80

Figure 3. Particle launches for southward IMF. In this figure all items are at or projected into the y = 0

plane. The thin lines are magnetic field lines begun at y= 0 at the sunward boundary. Particles were

launched on planes whose locations are indicated by the heavy lines. The other curves are fits to the

magnetopause and bow shock and the x = 0 and y = 0 planes. The small circle represents the location of

the Earth. Note the presence of dipole tilt and B_.

enced different field configurations as time advanced. This

was done by interpolating linearly in time between snap-

shots of the simulation fields taken every four minutes.

Protons were launched every minute between simulation

hours 3.0 to 8.0, while 3He ions were launched only for

southward IMF. i.e. between hours 3 and 3.5. A total of 9.4

million protons were launched, as well as about 1 million

3He ions. High energy particles from the Sun reach the

Earth streaming along interplanetary magnetic field lines

[FhTckiger, 1990]. We theretbre launched our test particles

(protons and 3He ions) upstreana of the magnetosphere in

the solar wind. Figure 3 shows where they were launchedfor southward IMF. Particles were launched near the sun-

ward boundary on a plane in the solar wind at x = 15 RE

extending between -35 and 35 RE in v and in z. SEP

particles from a single distant source arriving at the Earth

along interplanetary field lines will an'ive either parallel to

or anti-parallel to the interplanetary field lines. Because the

IMF Bx was negative particles that enter the system from

the sunward direction were moving along magnetic field

lines. Particles that arc moving along field lines should enter

the simulation system at other locations where field lines are

directed into the system as ",veil. All locations at the side,

bottom or top boundary where field lines were directed into

the simulation region were presumed to be particle sources.

For example, for the southward IMF case particles were

launched along the top boundary, as well as the front

boundary as well as at x = 15 RE (Figure 3). Because

particle distributions were modified by interaction with the

bow shock we wanted to confine our launches to upstream

of the bow shock. We there_bre launched only in the region

x > - 11 RE near where the bow shock intersects the system

boundary; with this limit, however, some particles were

launched in the magnetosheath because the bow shock

position varied in time and this limit was an approximation.

[_1] The particles were distributed in velocity space as a

kappa distribution [Christon et al., 1988] with a _ coeffi-

cient of 0.5. The formula for a kappa distribution function is

F (E) _ (1 + E/_E,rV "-I where E is the energy and ET is

the thermal energy. For E>>E,r this becomes a power law

with a coefficient of -(_ + 1). The thermal energy used was

set to a value near 40 keV. The energy range of particleslaunched was between 0.1 and 50 MeV. Particles below

100 keV were not included in the distribution because our

study concerned particles above typical magnetospheric

energies; and particles above 50 MeV have Larmor radii

comparable to the system size also were not included. The

launched distribution was isotropic except for the fact that

only particles with velocities into the simulation systemwere included.

[12] Particles reaching the outer boundaries of a box with

edges at x = 18, x = -t00, y = ±40 and z = ±40 were

removed as were those reaching a 4.5 RE radius spherecentered on the Earth which is outside the simulation inner

RICHARDET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL SSH 7 - 5

boundary at 3.5 RE. The particles reaching this boundary

were considered to have precipitated. Particle 'hits' were

collected at planar and spherical virtual detectors [,4shour-

Abdalla et al., 1993]. Particles that cross these surfaces have

the time, positions and velocities of their crossing recorded.

Particle fluxes and other quantities can be calculated from

these values. Note that in the results shown in this paper

flux at a virtual detector is the omnidirectional flux; i.e. the

contributions of all the particles crossing a given virtual

detector surface from any direction in a given region

(chosen to be 1 RE squares) are added together. The flux

at virtual detectors scale with the source in the upstream

solar wind. Because we launched particles from x > - 11 RE

only, we neglected particles that could arrive on open field

lines that reached the simulation boundary tailward of thebow shock. Because the E x B drift in the solar wind was

small compared to the velocities of the energetic particles,

they usually did not convect to these parts of the polar cap

either. This left part of the polar cap empty in our results. If

our system size in y and z had been large enough to include

all open field lines on the sunward side, the polar cap would

probably have been more completely filled.

[13] Since we carried out our calculations using a time

dependent IMF we must ask how our assumed time depend-

ence (Figure 1) influences the results. In this idealized

problem we want to show how particles enter the magneto-

sphere for a given IMF orientation. Therefore we want the

magnetosphere to reach a quasi-steady configuration con-

sistent with each IMF direction. However, trapped particles

can remain in the model magnetosphere for a long time

compared to the time between IMF orientations. Even after

the IMF reaches a quasi-steady state for a given IMF some

of the particles may have entered the magnetosphere when

the IMF had a different orientation. To help us understand

the effects of the time dependence on our results we carried

out a series of calculations of particle trajectories for which

the electric and magnetic fields were held constant. For

these runs we used the electric and magnetic fields from

single time steps in the MHD simulations. By comparing

the time dependent results with the results from thesesnapshots we can estinaate the significance of the time

dependence.

3. Calculation Results

[14] At the beginning ofthe particle calculations, at hour

3.0, the IMF was in a Southward orientation, and remained

so until hour 3.5 at which time the IMF began.its transition

to a dawnward (positlveBy) orientatioo. Recall that therewas a constant Bx throughout the entire simulation. At

hour 4.0 the IMF transition was complete. During thesouthward IMF conditionreconnection takes place on the

dayside and in the _agnetotail. Omnidirectional particlefluxes (.protons / area. time)during the in ter_al from hours

3.0 to 3.5 are shownqn_'Figure 4. The upper panel shows

the fluxes at the z = 0 pl/if/e and the lower panel shows the

y = 0 plane for the interval between hours 3.0 and 3.5. Fitsto the bow shock and magnetopause in the MHD simu-lation are shown as black curves. The dotted curves are the

inner boundary of the particle calculation at 4.5 RE. Nonzerofluxes appear just inside the inner boundary because the

fluxes are collected in 1 R 2 domains. One important feature

of the results at this and subsequent times was how

effective the magnetospheric magnetic fields were in shield-

ing the magnetosphere from the high energy solar protons.

The bow shock and the magnetopause reflected most

incoming protons. Note that the omnidirectional flux of

particles upstream of the bow shock was often greater than

the incident flux of particles launched. This was because of

the contribution of particles reflected from the bow shock;

recalling that particles passing through virtual detector

planes in either direction were added to compute the

omnidirectional flux, whereas in the incident flux all ions

cross an upstream virtual detector in the same direction.

There is a region of low omnidirectional flux, relative to

adjacent magnetosheath and magnetospheric regions, just

outside the magnetopause on the dawn side. This region

contains open field lines that extend dawnward away from

the Earth and then southward to the bottom boundary where

particles were not launched during this interval. The 3He

ions we launched under southward IMF qualitatively fol-

lowed the distribution of the protons but their flux within

the magnetosphere was generally lower relative to their

upstream abundance.

[15] A significant number of ions did penetrate the

magnetosphere. We have observed two entry mechanisms

for the ions we launched. As we will see later, ions with

energies greater than about 10 MeV have Larmor radii large

enough that they can directly penetrate the magnetosphere

on the dayside, while lower energy ions moved along open

field lines into the magnetosphere. The coefficient of

adiabaticity _ the square root of the ratio of the particle

Larmor radius to the field line curvature [Biichner and

Zelenyi, 1989] for these energetic particles often fell to

values of around 1 or less and they can experience non-

adiabatic behavior. This _ is not to be confused with the

coefficient in the distribution function. In our simulation the

directly penetrating particles were energetic enough to

experience non-adiabatic behavior over large regions of

the magnetosheath and magnetosphere. The locations of

open field lines were of primary importance in determining

particle entry for the majority of the particles, which were at

energies below 1 MeV. Where the magnetic field was weak

or had a small radius of curvature entry was enhanced.

[16] Note the effect of dipole tilt and Bx in Figure 4.

Because of these factors the plasma sheet was warped such

that it was lower (in z) near midnight than on the dusk or

dawn flanks and parts of it fell below z = 0. In the magneto-

tai['_b_etween hours 3.0 and 3.5 the protons were mainly

confined to the plasma sheet while the lobes were nearly

empty. Protons in this plasma sheet were confined within a

band around 5 RE high in z, but were spread out all along the

pla_sma sheet in y, reflecting the thinness of the plasma sheet

forSputhward IMF. During this time interval (hours 3.0 to

4.0)-;the protons entered mainly on the front side of the

magnetosphere, often through the northern cusp region,

visibie:]n Figure 4 nearz = 6, x = 3 RE. The weak field

anki_bl6en field lines at the northern cusp allowed particles to

access the inner magnetosphere. Once inside the magneto-

sphere, they sometimes became quasi-trapped and began

drifting around the Earth. While a few protons remained

trapped over a relatively long term (hours) most of them

reached the inner boundary or entered the plasma sheet and

SSH 7 - 6 RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL

Proton flux hours 3.0 to 3.5

at Z=0 (upper) and Y=0 (lower)

_o ,--

_ , .............. , .............. , .............. , g O.0

o

A

Ill

N

o

|

o¢N

|

15 0 -15 -30

15 0 -15 -30

X (R,=)

Figure 4, Omnidirectional particle fluxes accumulated at virtual detectors. The upper panel shows thefluxes at the z = 0 plane and the lower panel shows the v = 0 plane for the interval between hours 3.0 and3.5. Fits to the bow shock and magnetopause in the MHD simulation are shown as black curves. Thedotted curves are the inner boundary, of the particle calculation at 4.5 RE. Nonzero fluxes appear justinside the inner boundary because the fluxes are collected in t R 2 domains. In the magnetosphere, theregions of highest flux had the order of a thousand hits (one particle can hit a virtual detector more thanonce) per domain at a virtual detector while the smallest fluxes could reflect a single hit.

were subsequently lost tailward or at the flanks. The particlesthat became trapped for long enough to completely circle theEarth were adiabatic for the most part and could be energizedby the changing local magnetic field responding to the 1MF.

The cusp, plasma sheet and the region of quasi-trappedparticles are clearly visible in Figure 4, bearing in mindthe effect of dipole tilt and consequent plasma sheet warping.The high omnidirectional flux of protons visible in the noon-

RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL SSH 7 - 7

Z

t_

a

Particle flux hour 3.0

at Z=0 (upper) and Y=0 (lower)

o

AILl

n" o

N

o

!

o¢_1

|

15

0 -15 -30

0 -15 -30

x

Figure 5. Omnidirectional particle fluxes accumulated at virtual detectors tbr a t_me independent case.

This calculation used a snapshot of the MHD at 3.0 hours. The format is the same as for Figure 4.

midnight meridian just above z = 0 inside the magnetopause

are quasi-trapped particles circulating around the Earth. Ions

m the equatorial region would probably have approached the

Earth more closely, and remain trapped longer, but were lost

at the inner boundary at 4.5 RE. It must be kept in mind that

for most of these particles the trapping is temporary and they

leave close field lines again later, frequently returning

upstream. While the ions often bounced wildly through the

magnetotail the overall motion was primarily dawn to dusk

in the direction of the gradient drift in the tail and trapped

particles circled the Earth in the expected clockwise sense. It

can be seen that onmidirectional ion fluxes (Figure 4) reach

levels comparable to their fluxes in the solar wind for the

quasi-trapping region and the cusp.

[17] To help evaluate the role of time dependence we

also ran particles in a snapshot of the fields from the MHD

simulation taken at 3.0 hours. The flux pattern for this case

is shown in Figure 5. Companng this to Figure 4, it can be

seen that the two patterns are remarkably similar. There

seems to be a decrease in penetration mto the magneto-

SSI]- 7 - 8 RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL

Particle flux hours 4.0 to 5.0

at Z=O (upper) and Y=O (lower)|

z

<[

o1ira

|

IM

=¢o

>-

(n

a

¢:)

15 0 -15

15 0 -15 -30

X (Rs)

Figure 6. Particle fluxes between hours 4.0 and 5.0. The format is the same as for Figure 2. Thisinterval had a steady dawnward IMF.

sphere in the time-independent case versus the timedependent case. This may mean that penetration isenhanced in the time dependent case, but the effect isevidently secondary in the case of a slowly varyingmagnetosphere,

[]s] Between hours 4.0 and 6.0 the IMF was dawnward.For this configuration open field lines extended through thedawn flank. This defined the primary entry region ,for theprotons. On the other hand there is a region with relatively

few or no particles just inside the dusk side magnetopausc inthe equatorial plane beginning at about 7 RE from the noon-midnight meridian and extending to the dusk side boundary(Figures 6 and 7). Once they entered the plasma sheet protonsspread out toward the dusk side. Omnidirectional fluxes inthe quasi-trapping region, the plasma sheet and the cuspdecreased considerably during the interval between simula-tion hours 4.0 and 5.0 (Figure 6). The examination of singleparticle trajectories indicated that particles tended to

RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL SSH 7 - 9

Particle flux hours 5.0 to 6.0at Z=0 (upper) and Y=0 (lower)

= , o xa o '_

_o ,..

_ gn_15 0 -15 -30 (:;

o

o_m

AtU

N

oI

o

|

15 0 -15 -30

X (R E)

Figure 7.interval had a Steady dawnward IMF:

approach the near Earth region from the magnetotail or on the

dayside due to direct penetration that was always present. As

can be seen by comparing Figure 4 and Figure 6 there was alower flux of trapped and quasi-trapped particles (betweenabout 9 R_ and the inner boundary) during the dawnward

IMF interval. For this configuration, protons can most

easily access the magnetotail from the dawn side flank,

but these protons most commonly exit down the .tail and

do not reach the inner magnetosphere. The location of

Particle-fluxes. between hours 5.0 and 6.0. The format is the same as for Figure 2. This

maximum flux in the plasma sheet (comparing Figures 4and 6) is now further from the Earth, as well as less

intense. Because the field lines in the magnetotail are no

longer as highly stretched protons bounce further from the

equatorial plane.

[19] The interval between 5.0 and 6.0 had a flux distri-

bution qualitatively similar to that of the previous hour

(Figures 6 and 7). The main difference is an overall decrease

in flux and a concentration of high flux to a localized region

SNI-I '7 - lO RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL

Particle flux hours 6.0 to 7.0

at Z=O (upper) and Y=O (lower)

i> B/ ll

ga.

o15 0 -15 -30

_o

15 0 -15 -30

X (R,=)

Figure 8. Particle fluxes between hours 6.0 and 7.0. The lbrmat is the same as for Figure 2. The first

half an hour of this interval was during the transition from dawnward to northward IMF and the second

half hour was for steady northward IMF.

on the dawn side that did not seem to correspond to any

strong localized entry in the MHD simulation. Examining

single particle trajectories indicates that transport in the

magnetotail remained primarily from dawn to dusk. For

the dawnward case the time independent simulation (not

shown) gave results similar to the time dependent case. As

was seen in the southward IMF case, however, magneto-

spheric fluxes in the time independent case seemed to be

reduced slightly overall compared to the time dependent

case. For both southward and dawnward IMF particles often

pai'tially orbit the Earth while mirror bouncing and then exit

the magnetosphere, usually tailward or back into the mag-

netosheath. Others precipitate at the inner boundaw after

being trapped for a while. If the inner boundary had been

closer to the Earth, these particles would presumably have

remained trapped for a longer period.

RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL SSH 7 - 11

Particle flux hours 7.0 to 8.0

at Z=0 (upper) and Y=0 (lower)

:g

Q

o15 _. 0 -15 -30

m

tern

m

U

m9m

tim

O

N

15 0 '15 -30

X (R s)

Figure 9. Particle fluxes between hours 7.0 and 8.0. The format is the same as for Figure 2. Thisinterval had'a steady northward.IMF.

[2o] From hour 6.0 to 6.5 the IMF changed from dawri-ward to northward, and then remainedsteady until hour 8.0.

The asymmetry due" to dipole tilt and iMF Bx caused moreintense magnetic reconnection to take place in the SouthernHemisphere, tailward of the cusp, and therefore most openfield lines extended southward. The examination of singleparticle trajectories indicated that the great majority of theions in the northern hemisphere entered from a southwarddirection. Particle entry on the dawn side decreased and

fluxes in the southern cusp increased as the field changed(FigiJr¢ 8). The plasma sheet flux decreased although themaximum moved close to the Earth. The lobes on the dawnside contained a low level of energetic particle flux. This

flux extends to the noon-midnight meridian plane below theplasma sheet.

[:_] The flux from hour 7.0 to 8.0 decreased overall. Themost dramatic feature is the high flux in the southern cusp(Figure 9). The magnetopause can be seen to be a strong

SSH 7 - 12 RICHARD ETAL.: INTERPLANETARY MAGNETIC FIELD CONTROL

Z

a

Particle flux hour 7:45

at Z=0 (upper) and Y=0 (lower)

a

o4$

oI

A

MJ

¢¢o

>-

o

oo4

15

1="

0 -15 -30 o

0 -15 -30

X (R a)

Figure !0. Onmidircctional particle fluxes accumulated at virtual detectors tbr a time independent case.

This calculation used a snapshot from the MHD simulation at 7 hours 45 rain. The format is the same as

for Figure 9.

barrier to particle entry at this time. Particles enter through

the southern cusp and high fluxes also occur on the dawn

side LLBL region, though in this case particle drifts across

the field and access to open field lines replaced convection

on newly opened field lines [Richard et al., 1994] as the

main entry processes. When we ran a time independent case

using a snapshot of the northward IMF magnetosphere, at

7 hours 45 rain. we obtained an interesting result. While the

results in the outer magnetosphere were comparable

between the time dependent and time independent cases,

there is much less flux in the inner magnetosphere in the

vicinity of the equatorial plane in the time independent case

(Figure 10). To understand this difference we examined the

panicles that occupied the inner magnetosphere in the time-

dependent case. We found that these were trapped or quasi-

trapped particles that had entered the inner magnetosphere

RICHARDETAL.:INTERPLANETARYMAGNETICFIELDCONTROL SSH 7- 13

during earlier times when the IMF orientation was dawn-

ward or southward. We conclude that thei:e were no trapped

or quasi-trapped particles observed during the quasi-steady

northward IMF simulation that were launched while the

IMF was northward.

[22] Although the ions were usually non-adiabatic and

could gain or loose energy due to magnetospheric electric

fields, the high energies of the launched particles relative to

the electric potential across the magnetosphere caused

energization within the magnetosphere to be of minor

importance overall. The exceptions were particles gradient

drifting around the Earth for a prolonged interval. These

particles experienced adiabatic heating as the magnetic field

changed. Waves in the inner magnetosphere that might heat

ions further did not play a role in this calculation; even

though there are expected to be MHD wave modes present

in the simulation, because the sampling of the MHD

simulation results every four minutes filtered out almost

all waves. To understand the basic physics of particle entry

it is instructive to examine the trajectories of single particles

in the model system. The particle trajectories to be dis-

cussed now are protons that all precipitated onto the inner

boundary. Particles of this type were chosen because trans-

port into the near Earth region is important for our results.

For southward IMF protons could access the inner magneto-

sphere near the northern cusp. One such proton (Figure 11)was launched at simulation time 3 hours and 32 min and

had an initial energy of 107 keV and a 25 ° pitch angle. This

particle began on a solar wind field line on the dawn side

and moved toward the magnetosphere. At the magnetopause

it experienced a brief interval with _ < 1 as it crossed from

solar wind to closed field lines. After travelling tailward on

the dawn side near the equatorial plane it was eventually

scattered into a nearly perpendicular pitch angle. As it

migrated toward the Earth and became trapped, which

occurred near midnight, _ fell below 1.5. It became trapped

and remained so for a prolonged period, finally precipitating

after simulation hour 10. This particle experienced adiabatic

heating while trapped and its final energy was 190 keV.

While this particle was on open field lines only very briefly,

it was the strongly curved field lines resulting from dayside

reconnection that led to a decrease of_ allow!ng the particleto enter.

[23] A 611 keV proton launched at6 hours 14 min

simulation time, during the transition to northward IMF, is

shown in Figure 12. As can be seen from its path in the solar

wind the particle's motion is mainly field aligned there with

a pitch angle of 27 °. This particle began on solar wind field

lines on the dawn side and reached the magnetopause where

it became trapped in the magnetopause-_current layer: with a

mainly perpendicular pitch angle. It experienced _ < 2 only

during one interval,:whidh is od_curved field lines in the

magnetosheath. While in the magnetopause current layer it

reached open field lines,that it:followed 'inward, and its-

pitch angle changedto greater than l_i0 °. L_/ter it gained

more parallel velocity and. precipitated. In Figure 13 we

have plotted the traj_ct0ry of a pioton of 390 keV launched

at 6 hours 26 min simulation time with an initial pitch angle

of 63 °. As one would expect from the IMF direction at this

time it approached the magnetosphere from the southern,

dawnward direction. It crossed into the magnetosphere on

the flanks of the magnetotail. Its large Larmor radius in the

solar wind is apparent, and this allows it to cross directlyfrom the solar wind to open field lines and finally to closed

field lines. It moves on closed field lines to the inner

boundary. Finally a definitely directly penetrating protonis shown that had an initial energy of 45 MeV and an initial

pitch angle of 85 ° (Figure 14). It was launched at simulationtime 6 hours and 45 min. It had a huge Larmor radius in the

solar wind that tightened as it crossed the bow shock and

magnetopause. This particle moved easily between different

field line types until it struck the inner boundary. It

. experienced _ < 2 throughout much of its time in the

magnetosphere.

[24] One way to demonstrate the magnetospheric config-

uration's control of the entry of high energy particles is to

plot the population of the inner magnetosphere and the

precipitation rate (Figure 15) as a function of time. The

numbers in this figure were computed assuming that

the upstream flux represents a total flux above I00 keV

of 2.5 x 10 s protons / m'- - s. This number is based on the

differential flux for a typical SEP event at 100 keV taken

from Gloeckler [1984]. The precipitation rate, i.e. precip-

itation onto the inner boundary at 4.5 RE, shows a fairly

systematic variation with IMF. Recall that the 1MF was

southward at first, then dawnward, and finally northward.

Also keep in mind that part of the flux in the polar cap on

open field lines that do not connect to the dayside has been

omitted. During southward IMF the precipitation rate was

relatively high, reflecting an abundance of open field lines

and efficient transport into the inner magnetosphere. The

rate decreased during the dawnward IMF interval and

finally falls to a very low level during steady northwardIMF. The trend is consistent with the decrease of open field

lines that occurred as the IMF changed from northward to

southward as shown in Figure 2.

[25] The number of protons at less than 7 RE (Figure 15)can be taken to reflect the population of the inner magneto-

sphere in the model. While some of these protons were

quasi-trapped in the inner magnetosphere, most of them

remained only briefly in the inner magnetosphere before

reaching the inner boundary or exiting the system, usuallytailward or duskward. Only about 1% of the test protons

remained in the inner magnetosphere for more than 15 min.

Some protons were observed to make a nearly complete

circle around the Earth then exit back into the magneto-

sheath. The initial increase of the population during south-

ward IMF was evidently due to the system filling with

• protons as the calculation proceeded; particles could take a

few minutes to reach this region. During southward IMF

most protons entered the inner magnetosphere on the day-side. A_er the IMF turned dawnward the number entering

the inner magnetosphere on the dayside decreased and

highest Concentration of arrival points (into the inner mag-

netosphere) was found dawnward of midnight. Evidently

these were particles that entered the magnetotail on the

dawnside open field lines and reached the inner magneto-

sphere. The overall population in the inner magnetosphere

decreased-during dawnward IMF as the region of particle

arrival moved tailward. As the IMF changed to northward,

the entry rate into the inner magnetosphere increased again,

with protons arriving primarily from the dawn side. During

this transition the number of particles in the inner magneto-

sphere increased, but this is due to the particles in the

SS[-I 7- 14 RICHARDETAL.:INTERPLANETARY MAGNETIC FIELD CONTROL

3o

v O

O

N

O

O

?20

....... I ......... I"'"""l ....... "1 .........

10 0 -10 -20 -30 -40 -50 -60 -70 -80

O

O

O

NO1--,t

O

i

O

0

x (RE)

30 20 10 0 -10 -20 -30

Y.usK _RE) DAW.

Figure 11. Proton trajectory shaded gray according to ficld line type. Shown are points along a particle

trajectory projected onto the z = 0 (top panel), y = 0 (middle panel) and x = 0 (bottom panel) planes.

Points where the particle was on closed field lines are dark gray and ones on solar wind field lines are

medium gray. Because the total number of points had to be decimated to make this plot, the small number

of points on open field lines are not shown. Filled circles along the trajectory in the top and bottom panels

indicate the locations of local minimums of _ where _ < 2. In the middle panel, these points are behind

the dense points where the particle is trapped and therefore are not shown. To limit the cluttering of the

figure a filled circle was only plotted if it _vas at least 1.6 RE away from the others.

RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL SSH 7- I5

Q

t

ztgQ

a '

O

|

Eo

>,0

Q o

0

o

v

No

I

Q

I

0

|

2O

,,,,.,,,,i,,,,,, ,,,,,,,,,l,,,,l,,,,l,,,,,,,,,i,,,,,,,,,l,,,,,,,,,

10 0

O

-10 -20 -30 -40

X (R E)

-SO

O

o

IDCo

NOq,.

|

O

N'|

OO)

|

( _J_,,.°, AF%..,, 0

'"'""'I'"'''"' '"' .... "'"''"l'""'"'I'""""

30 20 10 0 -10 -20 -30

: DUSK Y (Rs) DAWN

-60 -70 -80

Figure 12. Proton trajectory shaded gray accordingto field line type. Shown are points along a particletrajectory projected onto the z = 0 (top panel), y = 0 (middle panel) and x = 0 (bottom panel) planes.Points where the particle was on open field lines are light gray and ones on solar wind field lines aremedium gray. Filled circles indicate points that were local minimums of _ where _ < 2 and were morethan 1.6 RE apart.

SSH 7 - 16 RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL

O

0

<O |

O

i

>.O,m-

a O

O

O(_1'

NO

i

O

o

O

¢,,_.0

2O

)

" ;:'.

,,, ...... n....... ,,

10 0 -10 -20 -30 -40

o X (R E)

-50 -60

O

Ov-

%

NOv-

Q

0

O

|

..._.v-

:_¢,"-.. a.q

",.,_

...... "'1 ........ '1'"' .... ' ....... |

30 20 10 0 -10 -20 -30

DUSK Y (RE) DAWN

-70 -80

Figure 13. Proton trajectory, shaded gray according to field line type. Shown are points along a particle

trajectory projected onto the : = 0 (top panel), y = 0 (middle panel) and x = 0 (bottom panel) planes.

Points where the particle was on open field lines are light gray and ones on solar wind field lines are

medium gray. Filled circles indicate points that were local minimums of _, where _ < 2 that were more

than 1.6 R_ apart.

RICHARDETAL.:INTERPLANETARYMAGNETICFIELDCONTROL SSI-I 7 - 17

O

z !

-"i 17"ff*i / / ,.:"

".-i \k

riO-"

,I" o, _°

20 10 0 -10 -20 -30 -40 -50 -60 -70 -80

. X (R,)C_"

O

N

O

W

I_ o .

NO

O

i

l "'''""I''"'"'I '"" ............. I ......... I .........

_ 30 20 -10 0 -10 -20 -30

_; DUSK Y (Rs)- " DAWN

Figure 14.. Pmto_n t(ajector;y shaded gray according to field line type. Shown are points along a particle

trajectory projected onto the z = 0 (top panel), y = 0 {middle panel) and x = 0 (bottom panel) planes.

Points where the particle was on open field lines are light gray, ones on closed field lines are dark gray

and ones on solar wind field lines are medium gray. Filled circles indicate local minimums of _ where

_ < 2 that were more than 1.6 RE apart.

SSH 7- 18 RICHARDETAL.:INTERPLANETARYMAGNETICFIELDCONTROL

O

OIO

X

m

om

o

3

Precipitation rate (Ions/s), ..... ,.<._

3He dotted line (shifted up), protons solid line4.

?

I I ' I ' _ I ' '

4 5 6 7 8

0

X

0"m

Number of ions at less than 7 R E

o

,

' ' ' I ' ' ' 1 ' ' ' I ' ' ' I ' ' '3 4 5 6 7 8

Hours (UT)

Figure 15. Precipitation rate and population of the inner magnetosphere as a function of time. The gray

bands indicate the times when the IMF was changing. The top panel shows the precipitation rate onto the

inner boundary of the simulation/br an upstream flux of 2.5 x l0 s protons / m-" • sec. Data points are 15

rain apart. The bottom panel shows the number of particles between 7 RE and the inner boundary for the

same upstream flux, with data points every five minutes.

southern cusp, not trapped or quasi-trapped particles. As

steady northward IMF conditions continued few particles

reached the inner magnetosphere with most of these, briefly

entering near the southern cusp.

[26] The 3He ion abundance is enhanced during impul-

sive SEP events. We calculated 3He ion trajectories for

southward IMF only. The flux distribution for these par-

ticles was qualitatively similar to that of the protons that are

RICHARD ET AL.: INTERPLANETARY MAGNETIC FIELD CONTROL $SH 7 - 19

shown in Figure 4, but the fluxes within the magnetospherewere reduced relative to the upstream fux. For the purpose

of comparison with protons we plotted the population of the

inner magnetosphere and precipitation for these particles in

Figure 15 as if they had the same upstream flux as the

protons. It can be seen that they entered the inner magneto-

sphere and precipitated at a lower rate (relative to their

upstream flux) than the protons. This is consistent with the

role of _ in particle entry. For particles of the same energy

the velocity of a proton will be greater than that of an 3He

ion by a factor of the square root of the mass ratio. The mass

of an 3He ion is three times the mass of a proton while the

charge doubles. This leads to a proton having a Larnaor

radius 15% larger than an 3He ion of the same energy.

4. Conclusions

[_,7] We have seen that in our calculation high energy

particles' access to the magnetosphere was strongly con-

trolled by the IMF. For a steady proton source the onmidir-

cctional proton fluxes in some locations in the magnetotad

vaned by a factor of 100 as the IMF changed. Transport into

the inner magnetosphere varied by a factor of 5. A south-

ward IMF condition allowed the greatest access to the

magnetosphere of the IMF conditions studied, dawnward

IMF less, and northward IMF considerably less. The cusp

was an important entry region tbr the high energy particles

for northward and southward IMF, while the dawn side

flank was the dominant entry location for dawnward IMF.

Fritz et al. [1999] reported that energetic particles are

frequently observed in the cusp region. While they have

ruled out an SEP source for events seen on August 27, 1996

it is possible that some of these events are related to SEPs.

Relative to their initial high energy, the SEPs in our

calculations usually did not gam or lose much energy. The

exceptions were particles that remained trapped long

enough to gam or lose energy adiabatically during IMF

transitions. It was likely that because of our tuner boundary

at 4.5 RE some particles that otherwise would remain

trapped and possibly further energized are lost. We caneasdy estimate thzs energization. In being transported from

6 RE to 4 RE at midnight an equatorial pitch angle particle

conserving _ would increase in energy by a factor of 2.8.

The transport of SEPs in our calculation often involved non-

adiabatic motion. Particles usually entered the magneto-

sphere while they were not adiabatic. Non adiabatic motion

could also be nnportant for the transport of particles onto

trapped or quast-trapped paths.

[2s] Time-independent calculations gave results that were

quite similar to the time dependent ones in the outer

magnetosphere, even though the latter were obtained by

accumulating data through half an hour to an hour while the

magnetosphere was slowly varying. This indicates that for a

slowly varying magnetosphere a time independent calcula-

tion is adequate for modeling energetic particle entry. This

can be attributed to the fact that high energy particles

rapidly precipitated, became trapped or exited the magneto-

sphere. There were hints that particle penetration was

enhanced in the time dependent case, suggesting that a

rapidly varying magnetosphere could experience signifi-

cantly enhanced particle penetration. On the other hand,

trapped parttcles experienced the consequences of IMF

changes. These particles, however, remained a minor part

of the total population in the inner magnetosphere during

southward and dawnward IMF. The trapped particles were

affected by IMF changes largely through adiabatic changes

that affbcted the particle orbits by a relatively small amount

and changed their energies. During northward IMF, when

particles from the solar wind dxd not become trapped, the

trapped parttcle population consisted solely of particles that

had entered the magnetosphere during earher IMF orienta-

tions. The population of trapped particles was reduced in

our calculation, however, by the removal of particles at 4.5

RE from the Earth.

[29] Because IMF conditions typically undergo much

more rapid variauons than in this idealized case particle

entry into the magnetosphere may be even more complexthan in our results. In this calculation the residence time of

the vast nmjonty particles in the magnetosphere was much

less than the duration of transttions in the IMF (half an

hour). For rapid variations in the IMF, especmlly when a

shock strikes the magnetosphere, the entry process would

probably be modified. We argued in the introduction that if

the SEP proton flux m the solar wind during an intense

gradual proton event could easily enter the magnetosphere zt

would dominate the plasma sheet population in the energy

range above 0.1 MeV. Our model indicates that the SEP flux

within the magnetosphere does become comparable to the

solar wind flux m parts of the magnetosphere depending on

IMF onentatton. The near Earth magnetotail under south-ward IMF is one mstance of this.

[30] Acknowledgments, The authors would hke to thank L Zeleny,fi)r helping define the problem and V Peroomtan, D Schnvcr and GReeves for helpful d,scusslons "l'hls work was supported by NSF grantATM 98-19879 and NASA ISTP grant NAG5-6689 Computing resourceswere provided by the Natmnal Resource AIIocattons Committee (NRAC),the San Diego Supercomputer Center and the Office of Academic Comput-ing at UCLA.

[31] Arthur Richmond thanks Joan Feynman and another rev,ewer fortheir assistance m evaluaung manuscript 2001JA()00099

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M. Ashour-Abdalla, Department of Physics and Astronomy, University of

California at Los Angeles. Los Angeles, California 90095, USA.

M. EI-Alaoui and R. L. Richard, Institute of Geophysics and Planetary

Phys,cs, University of California at Los Angeles, Los Angeles, California

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R. J. Walker, Department of Earth and Space Science. University of

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